This is just supposition on my part, but I suspect there's something wrong systemically in Jaspers reman program. I would call them and ask to speak to a tech agent whom can talk intelligently to the issue, and be willing to review the repeated results of failure from an open mind.
My point is that perhaps Jasper has some dimension or spec wrong in their reman program process for that 5.3L engine series. Perhaps they are using the wrong bearings, wrong clearances, wrong torque, wrong parts, etc. Three engines having a similar failure mode is not your fault; it's clearly something they can't get right. They may not be sloppy; they may have copied over a dimension incorrectly into a machining center program, or used an old spec that is no longer valid, etc. Although many of us consider the Vortec engines all the same, there were a lot of minor changes as those engines went through evolutionary refinement over the years. Perhaps they have some outdated data for one or more parameters?
Case in point as my personal example ... I have three CV/GM cars; all span 2005 - 2007 in MY. I take them into the same place to get tires and alignment; always had good service. But we recently took one car to a different place for closer convenience. After alignment, car just didn't drive right; it seemed twitchy at steering inputs. I returned and complained, and was told it's "normal". Took it to our favorite shop, paid to have alignment, and then magically all is well. Went back to the "wrong" shop and asked for service manager. He was willing to sit down and look at the specs. Turns out they had the wrong chassis spec loaded into their program for our model cars! He was embarrassed and offered a free alignment, which I applied to another one of our cars. After the corrections were made, all was well. Think of all the customers they had blown off and yet it was actually their own arrogance that was the issue.
First you have to convince Jasper that they actually have something wrong; you'll have to bang around on the phone to get someone who's actually willing to listen. Don't get mad at them, just be persistent. You've got all the evidence you need to show that it's likely something in their reman process for that engine series that is not correct. It would be to their benefit to actually listen to you, as it will help reduce their warranty costs! In fact, if I were them, I'd want to track this engine all the way back to the employees who machined and assembled it. And, it would get a detailed tear-down with me in the room, so I can ascertain the specific failure (bearing likely, given the Pb but is it cam, main, rods?)